Enumerating Abelian Returns to Prefixes of Sturmian Words

We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian returns in Sturmian words. We determine the cardinality of the set $\mathcal{APR}_u$ of abelian returns of all prefixes of a Sturmian word $u$ in terms of the coefficients of the continued fraction of the slope, dependingly on the intercept. We provide a simple algorithm for finding the set $\mathcal{APR}_u$ and we determine it for the characteristic Sturmian words.Comment: 19page

Parallelizing multiple precision Taylor series method for integrating the Lorenz system

A hybrid MPI+OpenMP strategy for parallelizing multiple precision Taylor series method is proposed, realized and tested. To parallelize the algorithm we combine MPI and OpenMP parallel technologies together with GMP library (GNU miltiple precision libary) and the tiny MPIGMP library. The details of the parallelization are explained on the paradigmatic model of the Lorenz system. We succeed to obtain a correct reference solution in the rather long time interval - [0,7000]. The solution is verified by comparing the results for 2700-th order Taylor series method and precision of ~ 3374 decimal digits, and those with 2800-th order and precision of ~ 3510 decimal digits. With 192 CPU cores in Nestum cluster, Sofia, Bulgaria, the 2800-th order computation was ~ 145 hours with speedup ~ 105.Comment: arXiv admin note: text overlap with arXiv:1908.0930

Less is more: possibility and necessity as centres of gravity in a usage-based classification of core modals in Polish

In this paper we present the results of an empirical study into the cognitive reality of existing classifications of modality using Polish data. We analyzed random samples of 250 independent observations for the 7 most frequent modal words (móc, można, musieć, należy, powinien, trzeba, wolno), extracted from the Polish national corpus. Observations were annotated for modal type according to a number of classifications, including van der Auwera and Plungian (1998), as well as for morphological, syntactic and semantic properties using the Behavioral Profiling approach (Divjak and Gries 2006). Multiple correspondence analysis and (polytomous) regression models were used to determine how well modal type and usage align. These corpus-based findings were validated experimentally. In a forced choice task, naive native speakers were exposed to definitions and prototypical examples of modal types or functions, then labeled a number of authentic corpus sentences accordingly. In the sorting task, naive native speakers sorted authentic corpus sentences into semantically coherent groups. We discuss the results of our empirical study as well as the issues involved in building usage-based accounts on traditional linguistic classifications

Abelian combinatorics on words: a survey

We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on abelian equivalence, which is the equivalence relation defined in the set of words by having the same Parikh vector, that is, the same number of occurrences of each letter of the alphabet. In the past few years, there was a lot of research on abelian analogues of classical definitions and properties in combinatorics on words. This survey aims to gather these results.(c) 2022 Elsevier Inc. All rights reserved